Displacement convexity of generalized entropies

摘要: We investigate the m-relative entropy, which stems from Bregman divergence, on weighted Riemannian and Finsler manifolds. prove that displacement convexity of entropy is equivalent to combination a lower Ricci curvature bound weight function. use this show appropriate variants Talagrand, HWI logarithmic Sobolev inequalities, as well concentration measures. also gradient flow produces solution porous medium equation.